4 Ways to Represent Motion

4 Representations of Motion Verbal models (language) Mathematical models (equations) Graphs Diagrams(motion maps)

1. Language scalar – a quantity with only magnitude (a numeric value) but no direction (ex. time) vector – a quantity with magnitude and direction time interval (t) – a length of time SI unit is seconds (s) Scalar

position (x) – the location of an object with respect to an origin SI unit is meters (m) vector displacement (Δx) – change in position Δ Delta means change in Δx = xf – xi Ex: Stew runs 4m to the right of his home then 7m left. What is his displacement from his home?

average speed – the total distance traveled in an amount of time (Ex: 3 cm/s) SI unit is meters second Scalar speed = distance or v = d time t

average velocity (vavg) – total displacement of an object in an amount of time Speed with a direction (Ex: 3 cm/s south) SI unit is meters second Vector vavg = displacement or vavg = Δx time t

2. Mathematical Models(Equations) speed = distance or v = d time t velocity = displacement or v = Δx time t

Steps to Solve a Problem Draw a diagram of the situation Identify given variables and unknowns Convert Units Write equation and WRITE IT without numbers Substitute values and solve Box answer with units (and direction)

Example: A man runs 50 m to the west in 10.0 s, and then 30 m to the south in 6.0s. What is the magnitude of his average speed? (5 m/s) Is this the same as his average velocity? If he continues to run at this average speed, how far will he have travelled in 20 minutes? (6000m)

Turn to Pg 44 in your text book.